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### Fritzsche Formula at Standard Conditions Equation and Calculator

Fluids Engineering and Design Resources

Fritzsche Formula for Pressure Change at Standard Conditions Equation and Calculator

The Fritzsche formula uses the friction factor f calculated from the following equation:

Equation 1

*F = 0.02993 ( T _{s} / ( P_{s} Q_{s} ) ^{1/7}*

where:

f = friction factor

*T _{s}* = temperature at standard conditions, °R

*P*= pressure at standard conditions, psia

_{s}*Q*= volume flow rate at standard conditions, SCFM

_{s}The Fritzsche formula for pressure drop then becomes

Equation 2

ΔP = ( 9.8265 x 10^{-4} ) T L / ( P d^{5} ) ( P_{s} Q_{s} / T_{s} )^{1.857}

where:

*ΔP *= pressure drop, psi

L = pipe length, ft

d = pipe inside diameter, in

T = airflow temperature, °R

P = average air pressure, psia

*Q _{s}* = volume flow rate at standard conditions, SCFM

*P*= pressure at standard conditions, psia

_{s}*T*= temperature at standard conditions, ◦R

_{s}And in terms of flow rate and the upstream and downstream pressures, this becomes

Equation 3

Q_{s} = 29.167 T_{s} / P_{s} [ (
P_{1}^{2} - P_{2}^{2} ) d^{5} ) / ( T L )] ^{0.538}

where:

* Q _{s}*= volume flow rate at standard conditions, SCFM

*= pressure at standard conditions, psia*

P

P

_{s}*= upstream pressure, psia*

P

P

_{1}*= downstream pressure, psia*

P

P

_{2}*= pipe length, ft*

L

L

*= pipe inside diameter, in*

d

d

*T*= temperature at standard conditions, °R

_{s}*T*= airflow temperature, °R

The preceding formulas can be used for the flow of air at standard conditions and any flowing temperatures. When standard conditions of 14.7 psia and 60°F are used along with a flowing temperature of 60°F, the preceding formulas can be simplified as follows:

Equation 4

*ΔP =* L Q_{s}^{1.857} / ( 1480 P d^{5} )

where:

*ΔP *= pressure drop, psi

L = pipe length, ft

Qs = volume flow rate at standard conditions, SCFM (see equation 5)

d = pipe inside diameter, in

P = average air pressure, psia

Equation 5

Q_{s} = 1 / 35 [ *( P _{1}^{2} - P_{2}^{2} ) d^{5} ) /* L ]

^{0.538}

where:

Q_{s} = volume flow rate at standard conditions, SCFM

*P _{1}* = upstream pressure, psia

*P*= downstream pressure, psia

_{2}L = pipe length, ft

d = pipe inside diameter, in

Where air pressures are low and close to the atmospheric pressure
such as in ventilating work and in airflow through ducts, we can modify
the Fritzsche formula to calculate the pressure drops in in H_{2}O. Since
1 in of water column is equal to 0.03613 psi, the pressure loss can be
expressed as follows:

Equation 6

h = L Q_{s}^{1.857} / ( 785 d^{5} )

where h is the pressure drop measured in in H_{2}O.

Equation 7

Q_{s} = ( 785 h d^{5} / L )^{0.538}

Related:

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- Gas Flow Rate Through Orifice Equations and Calculator per. ISO 5167
- Low Pressure Flow Oliphant and Spitzglass Formula and Calculator

Reference:

- Piping Calculations Manual,

E. Shashi Menon

SYSTEK Technologies, Inc